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Worksheet Grade 7 Engineering & Design

Cattail Marsh Pump Station: Flow Rate and Design Constraints

A grade 7 engineering worksheet where students size a fictional stormwater pump station, converting flow units and applying the continuity equation to a constraint.

Objectives

  1. Students will convert a pump station's flow rate between gallons per minute, million gallons per day, and cubic feet per second.
  2. Students will apply the continuity equation to find the velocity of water moving through a pipe of known area.
  3. Students will identify design constraints that limit an engineering solution, such as a flow requirement and a budget.

Vocabulary

Pump station
A pump station is a building full of powerful pumps that push water through pipes or lift it uphill. Pumps give water the extra push that gravity alone cannot provide.
Flow rate
Flow rate measures how much water moves past a point in a certain amount of time, like gallons per minute through a garden hose. Bigger pipes and stronger pushes give bigger flow rates.

Also: continuity equation

Teacher overview

Engineers sizing a stormwater pump station have to move between several units of flow (gallons per minute, million gallons per day, cubic feet per second) and check that a proposed design meets both a performance requirement and a budget constraint. This worksheet uses a fictional neighborhood pump station to walk students through those single-step conversions and one application of the continuity equation, the same reasoning tools a real design engineer uses before recommending a pump size.

Cattail Marsh Pump Station: Flow Rate and Design Constraints — Grade 7 Engineering & Design
Name: ____________________________ Date: ______________

Student Worksheet

The fictional Cattail Marsh neighborhood floods during heavy storms, and engineers are sizing a pump station to move floodwater into a retention pond. The station has two identical pumps. Each pump, running alone, moves water at a rate of 500 gallons per minute (gpm). Use the following facts for all items:

  • 1 million gallons per day (MGD) equals 694 gallons per minute (gpm).
  • 1 cubic foot per second (cfs) equals 448.8 gallons per minute (gpm).
  • The continuity equation: flow (Q) = cross-sectional area (A) × velocity (V).
  1. If one pump moves 500 gpm, how many gallons does it move in 10 minutes?
  2. If both pumps run at the same time, what is the station's combined flow rate, in gpm?
  3. Using your answer to item 2, how many gallons would both pumps together move in one hour (60 minutes)?
  4. Convert the station's combined flow rate from item 2 into million gallons per day (MGD), using the fact that 1 MGD equals 694 gpm. Round to the nearest hundredth.
  5. A regional engineer requires the station to move at least 1.3 MGD during a major storm. Convert 1.3 MGD into gpm using the same 694 gpm-per-MGD fact. Is one pump (500 gpm) enough on its own? Are both pumps together (from item 2) enough?
  6. Convert the station's combined flow rate (1,000 gpm) into cubic feet per second (cfs), using the fact that 448.8 gpm equals 1 cfs. Round to the nearest hundredth.
  7. If pump run-time and gallons pumped are proportional, and one pump moving at 500 gpm runs for 15 minutes, how many gallons are pumped? What is the constant of proportionality, in gallons per minute?
  8. The outlet pipe leaving the pump station has a cross-sectional area of 2 square feet. Using the continuity equation Q = A × V, and your answer from item 6 as Q (in cfs), calculate the velocity V of the water moving through the pipe, in feet per second. Round to the nearest hundredth.
  9. A flooded street holds an estimated 45,000 gallons of stormwater that must be pumped out. If both pumps run together at their combined rate from item 2, how many minutes will it take to clear the flooding?
  10. Explain in one or two sentences why engineers often design a pump station with two smaller pumps instead of one larger pump that could do the same total job alone.
  11. A fictional budget constraint: running both pumps continuously would cost about $2,400 per month in electricity, but the budget allows only $2,000 per month. Using this constraint, describe one design change engineers might consider that would still protect the neighborhood during major storms.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: 5,000 gallons.
    500 gpm × 10 min = 5,000 gallons.
  2. Answer: 1,000 gpm.
    500 gpm + 500 gpm = 1,000 gpm.
  3. Answer: 60,000 gallons.
    1,000 gpm × 60 min = 60,000 gallons.
  4. Answer: 1.44 MGD.
    1,000 gpm ÷ 694 gpm/MGD ≈ 1.44 MGD.
  5. Answer: 902.2 gpm.
    1.3 MGD × 694 gpm/MGD = 902.2 gpm is required. One pump (500 gpm) falls short of 902.2 gpm, but both pumps together (1,000 gpm) exceed it.
  6. Answer: 2.23 cfs.
    1,000 gpm ÷ 448.8 gpm/cfs ≈ 2.23 cfs.
  7. Answer: 7,500 gallons.
    500 gpm × 15 min = 7,500 gallons, and the rate itself, 500 gal/min, is the constant of proportionality between run-time and gallons pumped.
  8. Answer: 1.12 ft/s.
    V = Q ÷ A = 2.23 cfs ÷ 2 sq ft ≈ 1.12 ft/s.
  9. Answer: 45 minutes.
    45,000 gallons ÷ 1,000 gpm = 45 minutes.
  10. Answer: Accept any reasoning that names redundancy or flexibility: if one pump fails or needs maintenance, the second pump can still handle part of the flow, and running only one pump during smaller storms can save energy compared with always running a single large pump at full capacity.
  11. Answer: Accept any reasonable design change consistent with the constraint, such as running both pumps only during major storms (as identified in item 5) rather than continuously, since continuous operation of both pumps costs more than the monthly budget allows, while running both pumps only when the flow requirement demands it would lower the average monthly cost.

Differentiation

Support (below grade level)

Provide the two conversion facts as labeled arrow rules on a printed strip ("gpm → MGD: divide by 694" and "gpm → cfs: divide by 448.8"), and give students the numerator and denominator of each division already set up (for example, "1,000 ÷ 694 = ___") so they complete only the final division.

Extension (above grade level)

Ask students to calculate what pipe cross-sectional area would be needed to keep the velocity from item 8 at or below 1.0 ft/s, using the same flow rate, and explain in one sentence why engineers might want to limit pipe velocity in a real stormwater system.

ELL supports

Pre-teach pump, flow rate, and velocity using a simple diagram of two pumps feeding one pipe with an arrow showing water moving through it. Allow item 10 to be answered with a labeled sketch showing one pump running versus two pumps running, in addition to or instead of a written sentence.

Extensions

Have students research a real stormwater pump station in their own community, either from a public works website or by contacting the local public works department, and compare its number of pumps and purpose with the Cattail Marsh station in this worksheet.